1. Field
A method for forming a double-curved structure and a double-curved structure formed using the same are disclosed herein.
2. Background
Surfaces may be flat, with no curvature in any direction. The overwhelming majority of man-made surfaces are flat, such as sheets of paper, cloth, plywood, and metal.
Further, a surface may have single curvature, that is, curvature along one axis, but not along the other axis. A cylinder, for example, has curvature around its circumference, but has no curvature parallel to its central longitudinal axis. A cone is another example of a single-curved surface. Single-curved surfaces may be formed by simply rolling a flat starting material into a desired shape.
Furthermore, a surface may be double-curved, with curvature along two axes. The curvatures may both be in a same direction, like a bowl (with both curvatures concave upward) or a dome (with both curvatures concave downward). Alternatively, the curvatures of a double-curved surface may be in opposite directions, concave upward along one axis, concave downward along the other, like a saddle-shaped surface, for example, a Pringles potato chip.
Unlike flat or single-curved surfaces, double-curved surfaces are a challenge to create from typical man-made flat starting materials. Many have experienced this first hand, as it is easy to gift wrap a package that is defined by flat or single-curved surfaces; however, smoothly wrapping a double-curved shape, a basketball, for instance, is a different story.
Creating a double-curved surface from a flat starting material requires the ability to selectively distort the starting material. For a saddle-shaped, double-curved surface, one needs to selectively either tighten up the middle of the material and/or stretch out the edges. For a dome or dish-shaped, double-curved surface, the opposite is required; it is necessary to tighten up the edges of the starting material and/or stretch out the middle.
Traditional methods of creating a double-curved shape from flat starting materials involves precise cutting and joining of flat pieces to attain a desired double-curved shape. The ancient art of tailoring uses this method to achieve the goal of using flat cloth to smoothly cover a double-curved human form.
Another commonly used method of creating a double-curved shape from flat starting materials involves use of highly stretchable materials to accommodate areas that need to be stretched out to create a double-curved surface. For example, a tube sock is a single-curved cylinder of stretchable fabric that relies on the stretchiness of its material to allow it to conform to the double-curved human foot.
These methods may be used in the construction of double-curved structures. Tent-like double curved tensile fabric structures, for example, make use of both of these methods in combination. Flat fabric panels may be cut and joined together with high precision, much like pieces that make up a perfectly tailored piece of clothing. The fabrics used may also be highly stretchable compared to traditional structural materials, such as steel, concrete, and wood. The downside to this kind of construction, however, is cost. Just as a tailored suit is too expensive for most people, a building built in an analogous way is beyond the budget of most prospective building owners. Further, unusual fabric materials and the large deformations they undergo as they stretch make analysis and design of these structures a difficult and very specialized endeavor, further escalating cost.